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Question
Carpenter A takes 15 minutes to fit the parts of a chair while Carpenter B takes 3 minutes more than A to do the same work. Working together, how long will it take for them to fit the parts for 22 chairs?
Solution
Time taken by A to fit a chair = 15 minutes
Time taken by B = 3 minutes more than A
= 15 + 3 = 118 minutes
∴ As 1 minute work = `1/15`
B’s 1 minute work = `1/15`
(A + B)’s 1 minutes work = `1/15 + 1/18`
`12/180 + 10/180 = 22/180`
= `11/90`
∴ Time taken by (A + B) to fit a chair
| 3 | 15, 18 |
| 5, 6 |
L.C.M = 3 × 5 × 6 = 180
= `1/(11/90)`
= `90/11` minutes
∴ Time taken by (A + B) to fit a chair
= `90/11 xx 22` = 180 minutes
= `180/60`
= 3 hours
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